I have a grid of ~48000 points, however this grid has this break which coincides with two different UTM zones (36S and 37S):

I don't know how this grid was obtained but it's pretty obvious to me that the problem is related with the junction zone of the two UTMs (and eventually was originally obtained in one UTM projection since the points of one side seems to be well-positioned - see next figure).

Is there any way I can fix this (I'm more into R but any suggestion would be great)?

did you try first re-projecting into lambert?
– Elio DiazOct 26 '17 at 16:24

What do you mean by "fix"? What you've got is not a regular grid. You could create a new grid in whatever projected coordinates you are showing. But those new grid points wouldn't sit exactly where the plots you showed are. Are those locations crucial?
– SpacedmanOct 26 '17 at 19:59

This grid was imported in Collect Earth to assign a land use class to each point. And in the Collect Earth, somehow, the grid was regular because I noticed that the land uses in the left-side of the grid match with the reality but in the right-side everything is wrong (that's why locations are crucial). So something happened maybe during the export... This is a also a mistery for me because I'm trying to predict what happened before came to my hands!
– Ana LeiteOct 26 '17 at 21:28

"The grid was imported in Collect Earth". Imported from where? A shapefile? And what have you got now? Another shapefile? How did you plot your blue dots in your picture? Can you show us their coordinates? The CRS they think they are? Was this in R, QGIS? etc.
– SpacedmanOct 27 '17 at 7:01